多功能工具箱

单元列表：

• Unit 1: Kinematics
  • Definition of average velocity:
    v=Δx/Δt
  • Definition og average acceleration:
    a=Δv/Δt
  • Displacement during 0 to t in a motion at constant accleration:
    Δx=v_0*t+1/2at^2
    Δx=(v^2-v_0^2)/2a
    Δx=1/2*(v_0+v)*t
• Unit 2: Dynamics
  • Equation for weight:
    F_g=mg
  • Hooke's law:
    F_s=kx
  • Equation for kinetic friction:
    F_f,k=μ_kF_N
  • Newton's second law of motion:
    F_net=ma
• Unit 3: Circular Motion
  • Calculation of centripetal acceleration:
    a_c=v^2/r
  • Frequency f, period T and speed v are related by:
    T=1/f=2πr/v
  • Calculation of centripetal force:
    F_c=ma_c=mv^2/r
  • Calculation of tangential acceleration:
    a_t=Δv/Δt
  • Law of universal gravitation:
    F_G=Gm_1m_2/r^2
    G=6.67x10^-11 Nm^2/kg^2
  • Calculation of graviational field strength:
    g=Gm_E/r^2
  • Graviational force as centripetal force:
    GMm/r^2=mv^2/r=m4π^2r/T^2
• Unit 4: Work and Energy
  • Definition of work:
    W=Fdcosθ
  • Definition of kinetic energy:
    K=mv^2/2
  • Work-energy principle:
    W_net=ΔK=mv_2^2/2-mv_1^2/2
  • Definition of gravitational potential energy:
    U_g=mgy
  • Definition of gravitational potential energy:
    U_g=-Gm_1m_2/r
  • Relationship between graviational force and potential energy:
    W_G=-ΔU_g
  • Definition of mechanical energy:
    E=K+U
  • Definition and calculation of average power:
    P=W/t=Fv
• Unit 5: Momentum
  • Position of center of mass:
    x_CM= (m_Ax_A+m_bx_b)/m_a+m_b
  • Definition of momentum:
    0=mv
  • Newtom's second law:
    F_avg=Δp/Δt
  • Definition of impulse:
    J=FΔt
  • Impulse-momentum theorem:
    J=Δp
  • Equations for elastic collisions:
    p_i=p_f,K_i=K_f
    or
    m_Av_A+m_Bv_B=m_Av_A'+m_Bv_B'
    1/2m_Av_A^2+1/2m_Bv_B^2=1/2m_Av_A'+1/2m_Bv_B'
  • Equations for explosions:
    p_i=p_f
    or
    (m_A+m_B)v_0=m_Av_A+m_Bv_B
• Unit 6: Rotation
  • Competition table(with Connection)

    Name	Translation	Rotation	Connection
    Postion	x	θ	x=rθ
    Velocity	v	ω	v=rω
    Acceleration	a	α	a_tan=rα or a_r=v^2/r=ω^2r
    Interia	m	I	I=Σmr^2
    Force	F	τ	τ=rFsinθ
    Newton's second law	ΣF=ma	Στ=Iα	/

  • Connection table(Only connection)

    Translation	Rotation
    KE=1/2mv^2	1/2Iω^2
    p=mv	L=Iω
    W=Fd	W=τθ
    ΣF=Δp/Δt	Στ=ΔL/Δt